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We study two famous interacting particle systems, the so-called Richardson's model and the contact process, when we add a stirring dynamics to them. We prove that they both satisfy an asymptotic shape theorem, as their analogues without…

Probability · Mathematics 2025-04-07 Régine Marchand , Irène Marcovici , Pierrick Siest

We are concerned with the supercritical contact process modified so that first infection occurs at a lower rate, it is known that the process survives with positive probability. Regarding the rightmost infected of the process started from…

Probability · Mathematics 2011-03-23 Achilleas Tzioufas

The stacked contact process is a stochastic model for the spread of an infection within a population of hosts located on the $d$-dimensional integer lattice. Regardless of whether they are healthy or infected, hosts give birth and die at…

Probability · Mathematics 2014-10-16 Nicolas Lanchier , Yuan Zhang

In the multitype contact process, vertices of a graph can be empty or occupied by a type 1 or a type 2 individual; an individual of type $i$ dies with rate 1 and sends a descendant to a neighboring empty site with rate $\lambda_i$. We study…

Probability · Mathematics 2018-03-06 Thomas Mountford , Pedro Luis Barrios Pantoja , Daniel Valesin

Let $\{Z_{m},m\geq 0\}$ be a critical branching process in random environment and $\{S_{m},m\geq 0\}$ be its associated random walk. Assuming that the increments distribution of the associated random walk belongs without centering to the…

Probability · Mathematics 2025-12-30 Vladimir Vatutin , Elena Dyakonova

The critical behavior of the contact process (CP) in heterogeneous periodic and weakly-disordered environments is investigated using the supercritical series expansion and Monte Carlo (MC) simulations. Phase-separation lines and critical…

Statistical Mechanics · Physics 2009-11-11 C. J. Neugebauer , S. V. Fallert , S. N. Taraskin

We consider a branching random walk in a random space-time environment of disasters where each particle is killed when meeting a disaster. This extends the model of the "random walk in a disastrous random environment" introduced by [15]. We…

Probability · Mathematics 2017-09-13 Nina Gantert , Stefan Junk

This review paper presents the known results on the asymptotics of the survival probability and limit theorems conditioned on survival of critical and subcritical branching processes in IID random environments. The key assumptions of the…

Probability · Mathematics 2011-10-28 Elena Dyakonova , Vladimir Vatutin , Serik Sagitov

We present simulation results for the contact process on regular, cubic networks that are composed of a one-dimensional lattice and a set of long edges with unbounded length. Networks with different sets of long edges are considered, that…

Statistical Mechanics · Physics 2015-05-13 R. Juhász , G. Ódor

We study the contact process on the complete graph on $n$ vertices where the rate at which the infection travels along the edge connecting vertices $i$ and $j$ is equal to $ \lambda w_i w_j / n$ for some $\lambda >0$, where $w_i$ are i.i.d.…

Probability · Mathematics 2016-06-14 Jonathon Peterson

We study branching processes in an i.i.d. random environment, where the associated random walk is of the oscillating type. This class of processes generalizes the classical notion of criticality. The main properties of such branching…

Probability · Mathematics 2007-05-23 V. I. Afanasyev , J. Geiger , G. Kersting , V. A. Vatutin

The contact process is a non-equilibrium Hamiltonian model that, even in one dimension, lacks an exact solution and has been extensively studied via Monte Carlo simulations, both in steady-state and time-dependent scenarios. Although the…

Statistical Mechanics · Physics 2025-04-15 Roberto da Silva , Eliseu Venites Filho , Henrique Almeida Fernandes , Paulo F. Gomes

We investigate the generalized contact process with two absorbing states in one space dimension by means of large-scale Monte-Carlo simulations. Treating the creation rate of active sites between inactive domains as an independent parameter…

Statistical Mechanics · Physics 2010-06-22 Man Young Lee , Thomas Vojta

We consider a symmetric finite-range contact process on $\mathbb{Z}$ with two types of particles (or infections), which propagate according to the same supercritical rate and die (or heal) at rate $1$. Particles of type $1$ can enter any…

Probability · Mathematics 2022-02-22 Mariela Pentón Machado

We study the contact process on a random bipartite connection hypergraph generated from two Poisson point processes, with mark-dependent connection thresholds. For asymmetric infection rates and asymmetric power law tail decays of the two…

Probability · Mathematics 2026-04-02 John Fernley , Christian Hirsch , Daniel Valesin

The pair contact process (PCP) is a nonequilibrium stochastic model which, like the basic contact process (CP), exhibits a phase transition to an absorbing state. The two models belong to the directed percolation (DP) universality class,…

Statistical Mechanics · Physics 2015-05-27 F. L. Santos , Ronald Dickman , U. L. Fulco

I study the absorbing-state phase transition in the one-dimensional contact process with mobile disorder. In this model the dilution sites, though permanently inactive, diffuse freely, exchanging positions with the other sites, which host a…

Statistical Mechanics · Physics 2015-05-13 Ronald Dickman

We study the contact process on a dynamic random~$d$-regular graph with an edge-switching mechanism, as well as an interacting particle system that arises from the local description of this process, called the herds process. Both these…

Probability · Mathematics 2023-10-02 Bruno Schapira , Daniel Valesin

Motivated by applications to COVID dynamics, we describe a branching process in random environments model $\{Z_n\}$ whose characteristics change when crossing upper and lower thresholds. This introduces a cyclical path behavior involving…

Probability · Mathematics 2026-01-14 Giacomo Francisci , Anand N. Vidyashankar

We study nonequilibrium phase transitions of reaction-diffusion systems defined on randomly diluted lattices, focusing on the transition across the lattice percolation threshold. To develop a theory for this transition, we combine classical…

Statistical Mechanics · Physics 2009-04-27 Man Young Lee , Thomas Vojta